Maxwell-like picture of General Relativity and its Planck limit

Abstract

We show that Geroch decomposition leads us to Maxwell-like representation of gravity in (3 + 1) metrics decomposition that may be perceived as Lorentz invariant version of GEM. For such decomposition we derive four-potential V µ and gravitational field tensor F µν that is associated with gravitational interaction. Next we show that gravitational four-current J µ derived for introduced four-potential produce energystress tensor and reproduce main General Relativity formula. Next we introduce valid Lagrangian and equations of motion that explains obtained results. At the end we introduce new approach to quantization of gravity that results in proper quantum values and is open to further generalization.

Gravity as field - field oriented framework reproducing General Relativity

“…In [1] we have also shown, that we may consider light behavior treating γ g as refracting index for light speed v c in vicinity of massive object.…”

“…This idea opens new area for exploration for origin of elementary particles rest energy as the energy stored in the spin. We have already shown in previous article [1], that rest energy E 0 of the massive body seems to be just Planck limit of the energy stored in the spin of massless particle approximated with Taylor series…”

“…In the previous article [1] we have shown, that for Schwarzschild case, curved spacetime is equivalent to flat manifold minimally coupled to some scalar field. It was also confirmed in [2] This scalar field changes the metric of the Stationary Killing Observer (SKO) -the observer located in the constant position with distance r to the source of gravity.…”

“…In our previous article we have also pointed, that if we switch to the gravitational field oriented approach, then we must carefully choose reference frame, because gravity seems to change light speed into 1 γg speed in distant observer reference frame. Now we will solve this enigma.…”